AdaFDR: a Fast, Powerful and Covariate-Adaptive Approach to Multiple Hypothesis Testing

Multiple hypothesis testing is an essential component of modern data science. Its goal is to maximize the number of discoveries while controlling the fraction of false discoveries. In many settings, in addition to the p-value, additional information/covariates for each hypothesis are available. For example, in eQTL studies, each hypothesis tests the correlation between a variant and the expression of a gene. We also have additional covariates such as the location, conservation and chromatin status of the variant, which could inform how likely the association is to be due to noise. However, popular multiple hypothesis testing approaches, such as Benjamini-Hochberg procedure (BH) and independent hypothesis weighting (IHW), either ignore these covariates or assume the covariate to be univariate. We introduce AdaFDR, a fast and flexible method that adaptively learns the optimal p-value threshold from covariates to significantly improve detection power. On eQTL analysis of the GTEx data, AdaFDR discovers 32% and 27% more associations than BH and IHW, respectively, at the same false discovery rate. We prove that AdaFDR controls false discovery proportion, and show that it makes substantially more discoveries while controlling FDR in extensive experiments. AdaFDR is computationally efficient and can process more than 100 million hypotheses within an hour and allows multi-dimensional covariates with both numeric and categorical values. It also provides exploratory plots for the user to interpret how each covariate affects the significance of hypotheses, making it broadly useful across many applications.